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Applied Analysis 3 (MATH 36203)

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Administrative Information

  1. Unit number and title: MATH 36203 Applied Analysis 3
  2. Level: H/6
  3. Credit point value: 20 credit points
  4. Year: 12/13
  5. First Given in this form: In similar form: 09/10
  6. Unit Organiser: Valeriy Slastikov
  7. Lecturer: Valeriy Slastikov and Isaac Chenchiah
  8. Teaching block: 2
  9. Prerequisites: MATH 20900 Calculus 2 or MATH 20200 Metric Spaces 2 (was Analysis 2)

Unit aims

  1. To introduce some of the methods of modern analysis that are useful in solving applied problems.
  2. To introduce some of the major applications of modern analysis

 

General Description of the Unit

Modern methods of analysis, especially of partial differential equations and the calculus of variations, have become increasingly significant in applied mathematics. 

This unit introduces some of these methods of modern analysis along with some of the major problems in the physical sciences that have been solved using these methods.

Relation to Other Units

This unit uses some methods and ideas introduced in Analysis 2 and Calculus 2.

Teaching Methods

Lectures - 3 per week, in which the lecturer will present the course material on the blackboard. Students are expected to attend all lectures, and to prepare for them by reading notes, handouts or texts, as indicated by the lecturer.

Homework assignments - several problem sheets will be handed out.

Learning Objectives

At the end of the course the student should be able to

  1. Use, in simple situations, the basic tools of partial differential equations and the calculus of variations, and
  2. Understand some key examples in the physical sciences in terms of these tools.

Assessment Methods

The final assessment mark for Applied Analysis 3 is calculated as follows:

  • 100% from a 2½-hour written examination in May/June
    More information is given below.

Summer Examination
The examination in May/June consists of a 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Calculators may NOT be used.

Award of Credit Points

Credit points are gained either by passing the unit, i.e. gaining a mark greater than or equal to 40; or gaining a mark of 30 or over on the examination, and also handing in reasonable attempts on at least 50% of the homework assignments.

Transferable Skills

  1. Increased understanding of the relationship between mathematics and the natural sciences.
  2. Development of problem-solving and analytical skills.

Texts

  1. Gelfand, I. M. and Fomin, S. V., Calculus of variations, Dover publications
  2. Lawrence C. Evans, Partial Differential Equations, AMS
  3. Markowich, Peter A., Applied partial differential equations: A visual approach, Springer
  4. Dacorogna, B., Introduction to the calculus of variations, Imperial College Press

Syllabus

  1. Preliminary results in analysis (functional spaces and basic theorems of PDEs and calculus of variations).
  2. Applications of analysis to important problems in materials science and physics.